Respuesta :
Answer:
P = 0.27R from the center
Explanation:
Given,
The radius of the uniform circular plate, R = 2R
The radius of the hole, r = R
The center of the smaller circle from the center is, d = 0.8R
The center of mass of a circular disc with a hole in it given by the formula
P = dr²/R² - r²
Where P is the distance from the center of mass located in the line joining the two centers opposite to the hole.
Substituting the given values in the above equation,
P = 0.8R x R² / 4R² - R²
= 0.27R³/R²
= 0.27R
Hence the center of mass of plate is at a distant P = 0.27R from the center
The center of mass is at 0.27R from the center of the larger circle.
Given information:
The radius of the uniform circular plate is r = 2R
The radius of the hole is r' = R
The center of the hole cut out is at d = 0.8R
Center of mass:
Let the mass of the uniform circular plate is M, the area of the plate is:
A = 4πR². The radius of the cut out is R, so the area cut out from the original plate is πR². Now the ss of the uniform plate that was contained in πR² area has been cut out, so the mass which has been cut out is:
[tex]m=\pi R^2\frac{M}{4\pi R^2}\\\\m=\frac{M}{4}[/tex]
So the mass of the remaining plate is [tex]\frac{3M}{4}[/tex]
If we assume the center of mass of the uniform circular plate as origin, and the center of the hole is at 0.8R then the center of mass CM of the plate after the hole cut out is given by:
[tex]M\times0-\frac{M}{4}\times0.8R=\frac{3M}{4}CM\\\\CM=-0.27R[/tex]
or
[tex]|CM|=0.27R[/tex]
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